My theory is nanotechnology. Well, at first. Nanotech eventually led to the production of hybrid quantum-organic computers, which can think and process much more rapidly than the Jurians' brains could, but could also grow and survive on the same materials that can sustain normal life. Jurian technology took the form of plant life because being able to harness light through photosynthesis was an advantage.

Of course, this is just my interpratation of what I see; who knows, maybe the show's creators put less thought into this than I did, and just wrote their storyboards thinking.. "Intelligent trees. That sounds neat!"